47 citations · 265 across the 22 of their papers we have counts for
5 papers · 2 filters
Well-posedness and decay to equilibrium for the Muskat problem with discontinuous permeability
Rafael Granero-Belinchón, Steve Shkoller
We first prove local-in-time well-posedness for the Muskat problem, modeling fluid flow in a two-dimensional inhomogeneous porous media. The permeability of the porous medium is de…
Suppression of blow up by a logistic source in D Keller-Segel system with fractional dissipation
Jan Burczak, Rafael Granero-Belinchón
We consider a two dimensional parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order . We obtain existence of global in time regula…
Global existence of weak solutions to dissipative transport equations with nonlocal velocity
Hantaek Bae, Rafael Granero-Belinchón, Omar Lazar
We consider 1D dissipative transport equations with nonlocal velocity field: \[ θ_t+uθ_x+δu_{x} θ+Λ^γθ=0, \quad u=\mathcal{N}(θ), \] where is a nonlocal operator give…
Global solutions for a hyperbolic-parabolic system of chemotaxis
Rafael Granero-Belinchón
We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.
On the fractional Fisher information with applications to a hyperbolic-parabolic system of chemotaxis
Rafael Granero-Belinchón
We introduce new lower bounds for the fractional Fisher information. Equipped with these bounds we study a hyperbolic-parabolic model of chemotaxis and prove the global existence o…